so the ratio is
[tex]\frac{|3x-2|^{n+1}}{(n+1)(n+1)!}\frac{n n!}{|3x-2|^n}= |3x-2|\frac{n}{(n+1)^2}[/tex]
What is the limit of that as n goes to infinity? If that is less than 1, the series will converge.